Abstract
Coherent evolution is punctuated by dynamical processes such as chemical exchange, conformational transformation, or site hopping in many important problems ranging from biomolecular function to ion trap quantum computation. One well-explored example is nuclear magnetic resonance (NMR) spectroscopy, where experimental development is grounded in decades-old theory, but structural dynamics are not easily integrated into this picture. Here, we introduce an approach that selectively excites NMR resonances that undergo chemical exchange while suppressing the signal arising from nondynamic components of the system. We show that for exchange rates spanning more than four orders of magnitude, one can still selectively excite spins undergoing exchange while suppressing static resonances. Generalizing this approach, to selectively excite (or selectively preserve) only members of an ensemble that have undergone exchange or rearrangement, has the potential to improve the analytical power of many spectroscopic techniques.
INTRODUCTION
Many important problems in biology, chemistry, and physics are best described by coherent evolution (Schrödinger’s equation and its generalizations) at short time, punctuated by dynamical processes such as chemical exchange, conformational transformation, or site hopping. While there are applications in many fields [e.g., exchange between sites in ion traps are important sources of decoherence in certain quantum computing architectures (1)], they have probably been most extensively explored in nuclear magnetic resonance (NMR). Recent studies have shown that RNA conformational transformations (including rare conformations) drive cellular activity (2), and studying this structural dynamics is useful for understanding function and assessing drug response. As another example, parahydrogen and ligand exchange on iridium-based catalysts enable substantial nuclear hyperpolarization on many molecules in solution (3–5) with limitations mostly related to the complexity of the exchange dynamics.The magnetic field in commercially available NMR spectrometers and thus also the spectral dispersion, has only doubled in the last four decades. The development of new experimental approaches (mostly multidimensional NMR) continues to expand the complexity of systems that can be studied. This progress has been driven by the robust theoretical foundations of magnetic resonance, specifically the density matrix framework developed over half a century ago. This made it possible to get away from perturbative treatments and to view the effects of spin evolution and radiofrequency fields as unitary transformations that could be combined in predictable ways. This led to the design of pulse sequences, which selectively remove the effects of certain interactions [dipolar line narrowing (6)], and to experiments that indirectly detect evolution of forbidden transitions [multidimensional spectroscopy (7, 8)].While this framework is immensely convenient for systems that undergo only spin evolution, it is not appropriate for more complicated systems that exhibit strong chemical exchange or relaxation. To describe effects such as chemical exchange, which is the foundation of the dynamic information that is the target for extraction from NMR data, one needs to use simulations that generally numerically integrate the equations of motion. While the theoretical framework for this is also decades old (9–14), recent work has found that the traditional implementation was founded on insufficient assumptions. Correcting this led to the development of a theoretical framework that routinely accelerates simulation time by an order of magnitude without loss of accuracy (15, 16). This facilitates computational design of approaches for magnetic resonance. Here, we use this formalism by developing an approach to selectively excite spins undergoing chemical exchange (Fig. 1), providing a route to expand the scope of systems that can be studied with magnetic resonance that would otherwise be obfuscated by spectral overlap of the dynamic and static components of the system.To the best of our knowledge, designing pulse shapes for the coherent manipulation of exchanging systems differentially from static systems has not yet been demonstrated in a manner that does not require selective manipulation of individual exchange sites. It is related to previous work showing compensation for relaxation using shaped pulses (17, 18) as well as work where shaped pulses are used in exchanging systems to improve saturation-type effects for chemical exchange saturation transfer type experiments (19–21). However, we will show that our approach does not use conventional saturation transfer to generate exchange-selective excitation. The development of excitation methods that require certain conditions to be met have been developed in magnetic resonance [for instance, the Bilinear Rotational Decoupling (BIRD) sequence that only generates excitation in the presence of a 13C spin (22)]; however, here the conditions are generated by the presence of chemical exchange in the system and that this is not a coherent interaction that conditionally permits excitation.
